(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 706722, 13810] NotebookOptionsPosition[ 685307, 13454] NotebookOutlinePosition[ 690354, 13564] CellTagsIndexPosition[ 690257, 13558] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[ CounterBox["BookChapterNumber"]], "BookChapterNumber", CounterAssignments->{{ "BookChapterNumber", 10}},ExpressionUUID->"290120f6-0d43-4bed-815c-e280536379b7"], Cell[TextData[StyleBox["Economic and Financial Applications", FontSlant->"Italic"]], "BookChapterTitle", CellChangeTimes->{{3.4841955305437803`*^9, 3.484195548636815*^9}, { 3.494934524580756*^9, 3.4949345348143744`*^9}, {3.495867168571354*^9, 3.4958671693353977`*^9}, {3.4963835258538475`*^9, 3.496383530081455*^9}, { 3.4964886355773106`*^9, 3.496488636279312*^9}, {3.503682917809148*^9, 3.5036829286043673`*^9}, {3.5044174325514517`*^9, 3.5044174408349257`*^9}, { 3.5061718013515873`*^9, 3.506171824689228*^9}, {3.5061722588223906`*^9, 3.50617226953961*^9}, {3.5061723209105*^9, 3.506172323640505*^9}, { 3.5065896626433744`*^9, 3.506589679257404*^9}, {3.5065897227502804`*^9, 3.506589725651885*^9}, {3.511325556366314*^9, 3.51132558274596*^9}, { 3.526865224655384*^9, 3.526865252563833*^9}, {3.5286033471833324`*^9, 3.528603348680935*^9}, {3.6532580191780376`*^9, 3.6532580252547283`*^9}, { 3.6809498437894297`*^9, 3.680949847500642*^9}},ExpressionUUID->"2f466bed-7788-4091-a563-\ a7ebce7e9a19"], Cell[CellGroupData[{ Cell["\<\ This notebook is part of the chapter 11 of the Book: Mathematica Beyond \ Mathematics: The Wolfram Language in the Real World.1st Edition. Chapman and \ Hall/CRC. by J. Guillermo S\[AAcute]nchez Le\[OAcute]n. It is Copyright by \ CRC, it is only for yourself. \ \>", "Author", CellChangeTimes->{{3.762577294671835*^9, 3.762577363398212*^9}, 3.7625774944729834`*^9, 3.762577545218973*^9, {3.762608074163491*^9, 3.762608086537633*^9}, {3.7626640708942165`*^9, 3.76266407340242*^9}, { 3.762664263811207*^9, 3.762664343477751*^9}, {3.7626643768826666`*^9, 3.762664475680722*^9}},ExpressionUUID->"a7ce139b-c398-468b-b82d-\ 016b5e63a571"], Cell[TextData[{ "The latest ", StyleBox["Mathematica", FontSlant->"Italic"], " versions include multiple capabilities related to economics and finance. \ The new functionality makes it easy to perform financial visualizations and \ to access both historical and real time data. The commands related to stock \ markets and financial derivatives would be especially useful to readers \ interested in investment portfolio management. Additionally, the functions \ for optimization, with applications in economics and many other fields, have \ been improved significantly. A new function to solve the Traveling Salesman \ Problem", StyleBox[" in a very efficient way has been included", FontSlant->"Italic"], ". All of these topics will be discussed in the sections below using real \ world examples. This chapter should be read along with Chapter 6, the one \ covering probability and statistics." }], "Epigraph", CellChangeTimes->{{3.5044170404050226`*^9, 3.5044172018122544`*^9}, { 3.504417259132533*^9, 3.5044174103901844`*^9}, {3.5044174582849236`*^9, 3.50441761190771*^9}, {3.5044176473887396`*^9, 3.504417804971753*^9}, { 3.504417865131194*^9, 3.5044178804030676`*^9}, {3.504418285150756*^9, 3.5044182928883696`*^9}, {3.504418664917487*^9, 3.5044186908059673`*^9}, { 3.504419615986252*^9, 3.504419631289879*^9}, {3.5044197149684258`*^9, 3.504419724671643*^9}, {3.504443690191*^9, 3.504443699551*^9}, { 3.5061722789464264`*^9, 3.5061723130636864`*^9}, {3.5061741859496117`*^9, 3.5061741922208223`*^9}, {3.5065878782313805`*^9, 3.5065878791517825`*^9}, {3.5065896960274334`*^9, 3.506589711736661*^9}, 3.506590439431139*^9, {3.5066898965341587`*^9, 3.5066899283569784`*^9}, { 3.5067097550156746`*^9, 3.50670975810448*^9}, {3.5067100212769423`*^9, 3.506710058233407*^9}, {3.506710142348755*^9, 3.5067103514203224`*^9}, { 3.507186026430828*^9, 3.5071866101370535`*^9}, {3.5071866552055326`*^9, 3.507186661258343*^9}, {3.5073846947625647`*^9, 3.5073847739327035`*^9}, { 3.5073848165987787`*^9, 3.507385029851153*^9}, {3.51132563391405*^9, 3.511325829319993*^9}, {3.5113308849652057`*^9, 3.511330933960724*^9}, { 3.51133157504385*^9, 3.5113315852150674`*^9}, {3.5162481034090223`*^9, 3.516248128727867*^9}, {3.516248160645523*^9, 3.516248279829732*^9}, 3.516253829504145*^9, {3.5286034007389326`*^9, 3.528603978220747*^9}, { 3.5286040083131995`*^9, 3.528604010871604*^9}, {3.528606558535883*^9, 3.5286066000943565`*^9}, {3.528606631013611*^9, 3.528606655162453*^9}, { 3.5286066856137066`*^9, 3.5286066889677124`*^9}, {3.5286074672522855`*^9, 3.5286075421324167`*^9}, {3.5287236526615725`*^9, 3.528723758866559*^9}, { 3.528723791299016*^9, 3.5287242973951054`*^9}, {3.5287855690919943`*^9, 3.528785638543316*^9}, {3.529122089325688*^9, 3.529122134846568*^9}, { 3.587372421546268*^9, 3.5873724570866137`*^9}, {3.6532580390660057`*^9, 3.653258084460711*^9}, {3.653258125869008*^9, 3.653258191964375*^9}, { 3.653258263282628*^9, 3.653258296935487*^9}, {3.653258364896852*^9, 3.653258517409998*^9}, {3.65325857168286*^9, 3.653258639116691*^9}, { 3.6532587027939587`*^9, 3.653258752319632*^9}, {3.653258793344936*^9, 3.653258830984448*^9}, {3.653258868604348*^9, 3.6532589241208677`*^9}, { 3.653258961010975*^9, 3.653258975251712*^9}, {3.6532590272641973`*^9, 3.6532590430918694`*^9}, {3.653259085485478*^9, 3.6532591348489323`*^9}, { 3.6532592059211807`*^9, 3.653259286414465*^9}, {3.653259682096559*^9, 3.653259687773541*^9}, {3.6552545677927203`*^9, 3.655254579549343*^9}, { 3.689216359355893*^9, 3.689216372819663*^9}, {3.6899350681075335`*^9, 3.6899350721087623`*^9}, {3.6901928105000577`*^9, 3.690192843331936*^9}, { 3.690192889898599*^9, 3.69019290441743*^9}, {3.6901929583535147`*^9, 3.6901929660269537`*^9}}, FontSlant->"Italic",ExpressionUUID->"365e4c85-e82d-4dc2-b17a-6e94b7c39965"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ CounterBox["BookChapterNumber"], ".", CounterBox["Section"], " Financial Information" }], "Section", CellChangeTimes->{ 3.511325952373009*^9, {3.511326000608294*^9, 3.5113260155999203`*^9}, 3.525780716075547*^9, {3.526866550979514*^9, 3.526866555035521*^9}, 3.528545059081527*^9, {3.5286135637318172`*^9, 3.5286135773038416`*^9}, { 3.6532593036813993`*^9, 3.6532593059325666`*^9}, {3.680949852237913*^9, 3.6809498528609486`*^9}, 3.688567894476845*^9},ExpressionUUID->"d55c0a0e-56f0-4add-820f-\ df84ddd9918a"], Cell[CellGroupData[{ Cell[TextData[{ CounterBox["BookChapterNumber"], ".", CounterBox["Section"], ".", CounterBox["Subsection"], " Introduction" }], "Subsection", CellChangeTimes->{ 3.503384149301452*^9, 3.5036629674488626`*^9, 3.5036630574610205`*^9, { 3.5036631670512133`*^9, 3.503663179406435*^9}, 3.5036633094558697`*^9, 3.50366334351073*^9, {3.526866281520241*^9, 3.5268662873702507`*^9}, { 3.526866318445505*^9, 3.5268663252003174`*^9}, {3.52860708241521*^9, 3.528607116454469*^9}, {3.5286071882769957`*^9, 3.528607188947797*^9}, { 3.5286432168920336`*^9, 3.528643228376629*^9}, {3.632068010560815*^9, 3.6320680151702576`*^9}, {3.6552531155920353`*^9, 3.6552531170740376`*^9}, 3.6885678977205925`*^9},ExpressionUUID->"32a7fd1f-5219-40f5-857f-\ 88ae2705d318"], Cell[TextData[{ StyleBox["Mathematica,", FontSlant->"Italic"], " as part of its computable data functionality, includes the command ", Cell[BoxData[ ButtonBox["FinancialData", BaseStyle->"Link", ButtonData->"paclet:ref/FinancialData"]],ExpressionUUID-> "3fffa7aa-df0d-484c-9da4-8da8c46adf53"], " to access finance-related information. Although in theory the program can \ display thousands of indicators, in reality the accessible ones are mostly \ those related to the US markets. Those readers who may need reliable access \ to other markets or real time financial data would probably be interested in \ taking a look at the Wolfram Finance Platform, a new product from Wolfram \ Research (the developers of ", StyleBox["Mathematica", FontSlant->"Italic"], ") that focuses on finance: ", ButtonBox["http://www.wolfram.com/finance-platform/", BaseStyle->"Hyperlink", ButtonData->{ URL["http://www.wolfram.com/finance-platform/"], None}, ButtonNote->"http://www.wolfram.com/finance-platform/"], ". 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In the \ website we can find that the symbol for the Standard & \ Poor\[CloseCurlyQuote]s 500 index, that includes the 500 largest public \ companies in terms of market capitalization that trade in either NYSE or \ NASDAQ is: ^GSPC (we can also use SP500). We can check it as follows:" }], "Item1", CellChangeTimes->{{3.5286142851988335`*^9, 3.5286143171944895`*^9}, { 3.632065213209977*^9, 3.63206531845693*^9}, {3.6320653837433434`*^9, 3.63206547158683*^9}, {3.6320655550199327`*^9, 3.6320655988698483`*^9}, { 3.6320658612588587`*^9, 3.6320659520588207`*^9}, {3.6320660140767975`*^9, 3.6320661027233677`*^9}, {3.6320662048805065`*^9, 3.632066295742144*^9}, { 3.632066335600894*^9, 3.632066342116729*^9}, {3.6320665626732483`*^9, 3.6320665974395456`*^9}, {3.632068129942768*^9, 3.632068158860351*^9}, { 3.6320682553329697`*^9, 3.632068287992019*^9}, {3.653261900890417*^9, 3.6532619547830877`*^9}, {3.653262023951745*^9, 3.653262123102804*^9}, { 3.6532621613251877`*^9, 3.6532622061182003`*^9}, 3.66414584943736*^9},ExpressionUUID->"074cdaab-b42a-4d1e-bedb-\ 1791e1158e0e"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FinancialData", "[", RowBox[{"\"\\"", ",", " ", "\"\\""}], " ", "]"}]], "Input", CellChangeTimes->{ 3.528544849621353*^9, {3.528545076834358*^9, 3.5285450951643906`*^9}, { 3.5286142721104107`*^9, 3.5286142733272123`*^9}, {3.632065488790216*^9, 3.632065510546524*^9}, {3.6320657253672795`*^9, 3.6320657483105817`*^9}, 3.6320658112105503`*^9, {3.6320659735904922`*^9, 3.6320659813069196`*^9}, 3.632066456123722*^9},ExpressionUUID->"85272ebb-0019-435b-b359-\ df4657ac2a30"], Cell[BoxData["\<\"S&P 500\"\>"], "Output", CellChangeTimes->{ 3.6802671716881695`*^9},ExpressionUUID->"65b31ad3-94ba-4777-ada5-\ 7b90d0122135"] }, Open ]], Cell["\<\ If we want to see the price (with a few minutes delay) we can type:\ \>", "Item1", CellChangeTimes->{{3.6320682992330627`*^9, 3.632068388027321*^9}, { 3.653262357068342*^9, 3.6532623742005463`*^9}},ExpressionUUID->"79d26f5a-e57a-4979-b23d-\ 6465f7ea9ece"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FinancialData", "[", "\"\<^GSPC\>\"", "]"}]], "Input", CellChangeTimes->{3.484913493497945*^9, 3.632066525560854*^9},ExpressionUUID->"05a33ce2-2565-41f3-8998-\ 76b534aaae34"], Cell[BoxData["2269.`"], "Output", CellChangeTimes->{3.512790027428431*^9, 3.516258885223945*^9, 3.5268652973047113`*^9, 3.5286155590470424`*^9, 3.63206652923279*^9, 3.632142111986763*^9, 3.65326237864489*^9, 3.662736907025592*^9, 3.662736954379874*^9, 3.675009567297208*^9, 3.675707899147175*^9, 3.6782340782632365`*^9, 3.680267184102214*^9, 3.6926858685460167`*^9},ExpressionUUID->"b2319fbd-2fad-4195-a2e5-\ bfea4c009e7d"] }, Open ]], Cell["\<\ We can also access historical data. In this example we show the trajectory of \ the S&P 500 index from January 1, 2000 to December 31, 2016.\ \>", "Item1", CellChangeTimes->{{3.484203689142292*^9, 3.484203743717414*^9}, 3.4845666385295496`*^9, {3.5100453457286263`*^9, 3.5100453461966267`*^9}, { 3.5286427942120433`*^9, 3.528642827181426*^9}, {3.528778151038172*^9, 3.528778153955377*^9}, {3.5291339744601545`*^9, 3.529133975380556*^9}, 3.632068533095685*^9, {3.653262395061453*^9, 3.653262432707028*^9}, { 3.653262487599081*^9, 3.653262489068598*^9}, {3.664145866046129*^9, 3.664145868486224*^9}, {3.664145944777152*^9, 3.664145955150778*^9}, { 3.6802672659059196`*^9, 3.680267270524927*^9}, {3.692685180448428*^9, 3.6926851854964156`*^9}},ExpressionUUID->"8befe711-f2ad-44f0-bb0b-\ b69b24209194"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DateListPlot", "[", RowBox[{ RowBox[{"FinancialData", "[", RowBox[{"\"\<^GSPC\>\"", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}], "]"}], ",", RowBox[{"Joined", "\[Rule]", 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LineBreakWithin -> False], Style[ Dynamic[ System`CandlestickChartDump`$lows$602271[ System`CandlestickChartDump`$scaledindicatorpos$602271]], 12, {{FontFamily -> "Helvetica"}, {FontFamily -> "Helvetica"}}, FontFamily -> "Times"], Style[ "C: ", 12, {{FontFamily -> "Helvetica"}, {FontFamily -> "Helvetica"}}, FontFamily -> "Times", LineBreakWithin -> False], Style[ Dynamic[ System`CandlestickChartDump`$closes$602271[ System`CandlestickChartDump`$scaledindicatorpos$602271]], 12, {{FontFamily -> "Helvetica"}, {FontFamily -> "Helvetica"}}, FontFamily -> "Times"], Style[ Dynamic[ System`CandlestickChartDump`$dates$602271[ System`CandlestickChartDump`$scaledindicatorpos$602271]], 12, {{FontFamily -> "Helvetica"}, {FontFamily -> "Helvetica"}}, FontFamily -> "Times", LineBreakWithin -> False]}}, ItemSize -> Automatic, Spacings -> {{0, 0, 1, 0, 1, 0, 1, 0, 1, 0}, 0}, Frame -> False], System`CandlestickChartDump`$highlightstyle$602271 = Directive[ AbsolutePointSize[5], GrayLevel[0]], System`CandlestickChartDump`$axishighlightmin$602271 = 5.3424450000000006`, System`CandlestickChartDump`$closemarkerQ$602271 = False, System`CandlestickChartDump`$timestampstyle$602271 = Directive[ GrayLevel[0.75], Opacity[0.25]], System`CandlestickChartDump`$bouncingballQ$602271 = True, System`CandlestickChartDump`$tooltipstyle$602271 = { FrameStyle -> GrayLevel[0.7], Background -> RGBColor[1, 1, 0.7], ContentPadding -> False}, System`CandlestickChartDump`$xmin$602271 = -17.5, System`CandlestickChartDump`$xmax$602271 = 269.5, System`CandlestickChartDump`$fastpos$602271 = True, System`CandlestickChartDump`$mouseQ$602271 = False, System`CandlestickChartDump`$tooltipvalue$602271, System`CandlestickChartDump`$tpp$602271 = CompressedData[" 1:eJxtVC1oW1EUfhM1MTUxXf7Tkrz77kvW7jGoCYSZZ2oyUwYR7WAxFYuZiYoJ g5qamphRqKmqmYkZhMCYiRkTMRENg5owqInpzM7O+U65F/bMx7333PN95zvn vsq7D2/ePwuC4E/AX3v1eNAmPOnVXv7D8u0nxmHrHOtUsHvBGPz8zTgtbiV8 72Im8bNXjFfjtwdy/m1fzl8zlkeWMVj8Yry77jMOs03Gq7SyDz6517t/4d4j 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18.15`4., 3 -> 18.53`4., 4 -> 18.54`4., 5 -> 18.28`4., 6 -> 18.56`4., 7 -> 18.93`4., 8 -> 19.02`4., 9 -> 18.76`4., 10 -> 18.21`4., 11 -> 17.35`4., 12 -> 16.77`4., 13 -> 16.26`4., 14 -> 16.17`4., 15 -> 16.89`4., 16 -> 16.44`4., 17 -> 16.18`4., 18 -> 16.13`4., 19 -> 16.28`4., 20 -> 15.95`4., 21 -> 16.17`4., 22 -> 16.02`4., 23 -> 15.64`4., 24 -> 14.91`4., 25 -> 15.27`4., 26 -> 15.25`4., 27 -> 14.45`4., 28 -> 14.94`4., 29 -> 14.82`4., 30 -> 14.67`4., 31 -> 14.9`4., 32 -> 14.85`4., 33 -> 15.05`4., 34 -> 14.74`4., 35 -> 14.49`4., 36 -> 14.62`4., 37 -> 14.49`4., 38 -> 14.65`4., 39 -> 14.5`4., 40 -> 14.11`4., 41 -> 14.02`4., 42 -> 14.12`4., 43 -> 14.42`4., 44 -> 14.64`4., 45 -> 14.51`4., 46 -> 14.52`4., 47 -> 14.94`4., 48 -> 15.1`4., 49 -> 14.43`4., 50 -> 14.27`4., 51 -> 14.36`4., 52 -> 14.31`4., 53 -> 14.07`4., 54 -> 13.64`4., 55 -> 13.88`4., 56 -> 13.35`4., 57 -> 13.07`4., 58 -> 12.89`4., 59 -> 13.44`4., 60 -> 13.68`4., 61 -> 13.48`4., 62 -> 13.12`4., 63 -> 13.13`4., 64 -> 13.28`4., 65 -> 13.43`4., 66 -> 13.06`4., 67 -> 12.83`4., 68 -> 13.05`4., 69 -> 12.97`4., 70 -> 13.18`4., 71 -> 13.49`4., 72 -> 13.33`4., 73 -> 13.79`4., 74 -> 13.66`4., 75 -> 13.99`4., 76 -> 14.54`4., 77 -> 14.52`4., 78 -> 14.68`4., 79 -> 14.05`4., 80 -> 14.38`4., 81 -> 14.38`4., 82 -> 14.07`4., 83 -> 14.05`4., 84 -> 14.18`4., 85 -> 13.93`4., 86 -> 14.1`4., 87 -> 14.07`4., 88 -> 14.27`4., 89 -> 14.62`4., 90 -> 14.69`4., 91 -> 14.6`4., 92 -> 14.71`4., 93 -> 14.71`4., 94 -> 15.03`4., 95 -> 15.03`4., 96 -> 14.97`4., 97 -> 15.26`4., 98 -> 15.29`4., 99 -> 14.18`4., 100 -> 14.6`4., 101 -> 14.63`4., 102 -> 14.18`4., 103 -> 14.17`4., 104 -> 14.08`4., 105 -> 14.1`4., 106 -> 13.71`4., 107 -> 13.8`4., 108 -> 13.64`4., 109 -> 13.78`4., 110 -> 13.93`4., 111 -> 13.98`4., 112 -> 13.98`4., 113 -> 13.89`4., 114 -> 13.64`4., 115 -> 13.3`4., 116 -> 13.2`4., 117 -> 12.95`4., 118 -> 12.88`4., 119 -> 12.76`4., 120 -> 13.05`4., 121 -> 12.75`4., 122 -> 13.74`4., 123 -> 13.96`4., 124 -> 13.83`4., 125 -> 13.61`4., 126 -> 13.37`4., 127 -> 13.37`4., 128 -> 13.43`4., 129 -> 13.85`4., 130 -> 13.95`4., 131 -> 14.17`4., 132 -> 13.99`4., 133 -> 13.99`4., 134 -> 13.89`4., 135 -> 13.9`4., 136 -> 13.69`4., 137 -> 13.75`4., 138 -> 13.73`4., 139 -> 13.12`4., 140 -> 12.99`4., 141 -> 13.12`4., 142 -> 13.11`4., 143 -> 13.15`4., 144 -> 13.06`4., 145 -> 13.16`4., 146 -> 13.63`4., 147 -> 13.24`4., 148 -> 13.17`4., 149 -> 13.14`4., 150 -> 13.1`4., 151 -> 13.16`4., 152 -> 13.05`4., 153 -> 12.94`4., 154 -> 12.77`4., 155 -> 12.45`4., 156 -> 12.35`4., 157 -> 12.22`4., 158 -> 12.3`4., 159 -> 12.3`4., 160 -> 12.3`4., 161 -> 12.63`4., 162 -> 12.47`4., 163 -> 12.54`4., 164 -> 12.5`4., 165 -> 12.77`4., 166 -> 12.76`4., 167 -> 12.97`4., 168 -> 12.77`4., 169 -> 12.94`4., 170 -> 12.67`4., 171 -> 12.56`4., 172 -> 12.51`4., 173 -> 12.4`4., 174 -> 12.51`4., 175 -> 12.33`4., 176 -> 12.61`4., 177 -> 12.71`4., 178 -> 12.68`4., 179 -> 12.7`4., 180 -> 12.66`4., 181 -> 12.86`4., 182 -> 12.46`4., 183 -> 12.17`4., 184 -> 11.74`4., 185 -> 11.27`4., 186 -> 11.39`4., 187 -> 11.53`4., 188 -> 11.29`4., 189 -> 12.09`4., 190 -> 12.32`4., 191 -> 12.48`4., 192 -> 12.66`4., 193 -> 13.18`4., 194 -> 13.61`4., 195 -> 13.55`4., 196 -> 13.28`4., 197 -> 12.72`4., 198 -> 12.32`4., 199 -> 12.15`4., 200 -> 12.1`4., 201 -> 12.19`4., 202 -> 12.38`4., 203 -> 12.56`4., 204 -> 12.38`4., 205 -> 12.69`4., 206 -> 12.17`4., 207 -> 11.8`4., 208 -> 11.3`4., 209 -> 11.16`4., 210 -> 10.18`4., 211 -> 10.1`4., 212 -> 9.58`3., 213 -> 9.29`3., 214 -> 9.28`3., 215 -> 9.42`3., 216 -> 9.2`3., 217 -> 9.1`3., 218 -> 8.58`3., 219 -> 7.99`3., 220 -> 8.61`3., 221 -> 8.32`3., 222 -> 8.17`3., 223 -> 8.02`3., 224 -> 7.84`3., 225 -> 7.65`3., 226 -> 7.81`3., 227 -> 7.57`3., 228 -> 7.58`3., 229 -> 7.44`3., 230 -> 7.74`3., 231 -> 7.94`3., 232 -> 7.5`3., 233 -> 7.81`3., 234 -> 7.28`3., 235 -> 7.35`3., 236 -> 7.01`3., 237 -> 6.93`3., 238 -> 6.76`3., 239 -> 6.71`3., 240 -> 7.2`3., 241 -> 7.1`3., 242 -> 7.15`3., 243 -> 7.28`3., 244 -> 7.66`3., 245 -> 7.44`3., 246 -> 7.15`3., 247 -> 6.92`3., 248 -> 7.39`3., 249 -> 7.27`3., 250 -> 7.51`3., 251 -> 7.57`3.], System`CandlestickChartDump`$dates$602271 = Association[ 1 -> 1, 2 -> 2, 3 -> 3, 4 -> 4, 5 -> 5, 6 -> 6, 7 -> 7, 8 -> 8, 9 -> 9, 10 -> 10, 11 -> 11, 12 -> 12, 13 -> 13, 14 -> 14, 15 -> 15, 16 -> 16, 17 -> 17, 18 -> 18, 19 -> 19, 20 -> 20, 21 -> 21, 22 -> 22, 23 -> 23, 24 -> 24, 25 -> 25, 26 -> 26, 27 -> 27, 28 -> 28, 29 -> 29, 30 -> 30, 31 -> 31, 32 -> 32, 33 -> 33, 34 -> 34, 35 -> 35, 36 -> 36, 37 -> 37, 38 -> 38, 39 -> 39, 40 -> 40, 41 -> 41, 42 -> 42, 43 -> 43, 44 -> 44, 45 -> 45, 46 -> 46, 47 -> 47, 48 -> 48, 49 -> 49, 50 -> 50, 51 -> 51, 52 -> 52, 53 -> 53, 54 -> 54, 55 -> 55, 56 -> 56, 57 -> 57, 58 -> 58, 59 -> 59, 60 -> 60, 61 -> 61, 62 -> 62, 63 -> 63, 64 -> 64, 65 -> 65, 66 -> 66, 67 -> 67, 68 -> 68, 69 -> 69, 70 -> 70, 71 -> 71, 72 -> 72, 73 -> 73, 74 -> 74, 75 -> 75, 76 -> 76, 77 -> 77, 78 -> 78, 79 -> 79, 80 -> 80, 81 -> 81, 82 -> 82, 83 -> 83, 84 -> 84, 85 -> 85, 86 -> 86, 87 -> 87, 88 -> 88, 89 -> 89, 90 -> 90, 91 -> 91, 92 -> 92, 93 -> 93, 94 -> 94, 95 -> 95, 96 -> 96, 97 -> 97, 98 -> 98, 99 -> 99, 100 -> 100, 101 -> 101, 102 -> 102, 103 -> 103, 104 -> 104, 105 -> 105, 106 -> 106, 107 -> 107, 108 -> 108, 109 -> 109, 110 -> 110, 111 -> 111, 112 -> 112, 113 -> 113, 114 -> 114, 115 -> 115, 116 -> 116, 117 -> 117, 118 -> 118, 119 -> 119, 120 -> 120, 121 -> 121, 122 -> 122, 123 -> 123, 124 -> 124, 125 -> 125, 126 -> 126, 127 -> 127, 128 -> 128, 129 -> 129, 130 -> 130, 131 -> 131, 132 -> 132, 133 -> 133, 134 -> 134, 135 -> 135, 136 -> 136, 137 -> 137, 138 -> 138, 139 -> 139, 140 -> 140, 141 -> 141, 142 -> 142, 143 -> 143, 144 -> 144, 145 -> 145, 146 -> 146, 147 -> 147, 148 -> 148, 149 -> 149, 150 -> 150, 151 -> 151, 152 -> 152, 153 -> 153, 154 -> 154, 155 -> 155, 156 -> 156, 157 -> 157, 158 -> 158, 159 -> 159, 160 -> 160, 161 -> 161, 162 -> 162, 163 -> 163, 164 -> 164, 165 -> 165, 166 -> 166, 167 -> 167, 168 -> 168, 169 -> 169, 170 -> 170, 171 -> 171, 172 -> 172, 173 -> 173, 174 -> 174, 175 -> 175, 176 -> 176, 177 -> 177, 178 -> 178, 179 -> 179, 180 -> 180, 181 -> 181, 182 -> 182, 183 -> 183, 184 -> 184, 185 -> 185, 186 -> 186, 187 -> 187, 188 -> 188, 189 -> 189, 190 -> 190, 191 -> 191, 192 -> 192, 193 -> 193, 194 -> 194, 195 -> 195, 196 -> 196, 197 -> 197, 198 -> 198, 199 -> 199, 200 -> 200, 201 -> 201, 202 -> 202, 203 -> 203, 204 -> 204, 205 -> 205, 206 -> 206, 207 -> 207, 208 -> 208, 209 -> 209, 210 -> 210, 211 -> 211, 212 -> 212, 213 -> 213, 214 -> 214, 215 -> 215, 216 -> 216, 217 -> 217, 218 -> 218, 219 -> 219, 220 -> 220, 221 -> 221, 222 -> 222, 223 -> 223, 224 -> 224, 225 -> 225, 226 -> 226, 227 -> 227, 228 -> 228, 229 -> 229, 230 -> 230, 231 -> 231, 232 -> 232, 233 -> 233, 234 -> 234, 235 -> 235, 236 -> 236, 237 -> 237, 238 -> 238, 239 -> 239, 240 -> 240, 241 -> 241, 242 -> 242, 243 -> 243, 244 -> 244, 245 -> 245, 246 -> 246, 247 -> 247, 248 -> 248, 249 -> 249, 250 -> 250, 251 -> 251], System`CandlestickChartDump`$OHLCQ$602271 = False, System`CandlestickChartDump`n$602271 = 287., System`CandlestickChartDump`$scaledindicatorpos$602271 = 1, System`CandlestickChartDump`$axespos$602271 = 5.3424450000000006`, System`CandlestickChartDump`$offset$602271 = 18., System`CandlestickChartDump`keyQ$602271 = True, System`CandlestickChartDump`$sign$602271 = 1}, { DynamicBox[Typeset`ToBoxes[ System`CandlestickChartDump`$fastpos$602271 = First[ MousePosition[{"Graphics", Graphics}, {True, 0}]]; System`CandlestickChartDump`$indicatorpos$602271 = If[System`CandlestickChartDump`$fastpos$602271 =!= True, Clip[ Ceiling[System`CandlestickChartDump`$fastpos$602271 - 0.5], { Ceiling[System`CandlestickChartDump`$xmin$602271], Floor[System`CandlestickChartDump`$xmax$602271]}], System`CandlestickChartDump`$indicatorpos$602271]; System`CandlestickChartDump`$scaledindicatorpos$602271 = Round[ Rescale[System`CandlestickChartDump`$indicatorpos$602271, { Ceiling[System`CandlestickChartDump`$xmin$602271], Floor[System`CandlestickChartDump`$xmax$602271]}, { 1, System`CandlestickChartDump`n$602271} - System`CandlestickChartDump`$offset$602271]]; System`CandlestickChartDump`$mouseQ$602271 = Not[ TrueQ[System`CandlestickChartDump`$fastpos$602271]]; System`CandlestickChartDump`keyQ$602271 = KeyExistsQ[ System`CandlestickChartDump`$dates$602271, System`CandlestickChartDump`$scaledindicatorpos$602271]; System`CandlestickChartDump`$ohlclabel$602271 = Grid[{{ Style[ "O: ", 12, System`CandlestickChartDump`$textstyle$602271, FontFamily -> "Times", LineBreakWithin -> False], Style[ Dynamic[ System`CandlestickChartDump`$opens$602271[ System`CandlestickChartDump`$scaledindicatorpos$602271]], 12, System`CandlestickChartDump`$textstyle$602271, FontFamily -> "Times"], Style[ "H: ", 12, System`CandlestickChartDump`$textstyle$602271, FontFamily -> "Times", LineBreakWithin -> False], Style[ Dynamic[ System`CandlestickChartDump`$highs$602271[ System`CandlestickChartDump`$scaledindicatorpos$602271]], 12, System`CandlestickChartDump`$textstyle$602271, FontFamily -> "Times"], Style[ "L: ", 12, System`CandlestickChartDump`$textstyle$602271, FontFamily -> "Times", LineBreakWithin -> False], Style[ Dynamic[ System`CandlestickChartDump`$lows$602271[ System`CandlestickChartDump`$scaledindicatorpos$602271]], 12, System`CandlestickChartDump`$textstyle$602271, FontFamily -> "Times"], Style[ "C: ", 12, System`CandlestickChartDump`$textstyle$602271, FontFamily -> "Times", LineBreakWithin -> False], Style[ Dynamic[ System`CandlestickChartDump`$closes$602271[ System`CandlestickChartDump`$scaledindicatorpos$602271]], 12, System`CandlestickChartDump`$textstyle$602271, FontFamily -> "Times"], Style[ Dynamic[ System`CandlestickChartDump`$dates$602271[ System`CandlestickChartDump`$scaledindicatorpos$602271]], 12, System`CandlestickChartDump`$textstyle$602271, FontFamily -> "Times", LineBreakWithin -> False]}}, ItemSize -> Automatic, Spacings -> {{0, 0, 1, 0, 1, 0, 1, 0, 1, 0}, 0}, Frame -> False]; 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Its members are known as chartists and their techniques are known \ as technical analysis. They closely study the past performance of stocks or \ indices to find trends and support and resistance levels. These people \ associate certain graph shapes to future markets ups and downs. Although \ there\[CloseCurlyQuote]s no sound mathematical theory justifying their \ predictions, all economic newspapers have a section dedicated to this type of \ analysis. \ \>", "Texto AM", CellChangeTimes->{{3.5291248915585365`*^9, 3.5291251338049603`*^9}, { 3.5291256252454176`*^9, 3.529125663434682*^9}, {3.5291257342148046`*^9, 3.5291257865372963`*^9}, {3.52912860576633*^9, 3.5291286067163315`*^9}, { 3.6532826693756523`*^9, 3.653282789964658*^9}, {3.6532828931008167`*^9, 3.653282972465555*^9}, {3.653283007905848*^9, 3.65328301028935*^9}, { 3.653283048631031*^9, 3.653283116345752*^9}, {3.653283157841483*^9, 3.653283158543145*^9}, {3.653283215492745*^9, 3.653283370248192*^9}, { 3.6532834031980877`*^9, 3.653283410205987*^9}, {3.653283511025185*^9, 3.653283635285274*^9}, {3.6552547881011477`*^9, 3.6552547934851575`*^9}, { 3.664150031951344*^9, 3.664150032493462*^9}, {3.689216887171082*^9, 3.689216908314291*^9}, {3.6892169453144073`*^9, 3.6892169615783377`*^9}},ExpressionUUID->"7c5eaaee-59f6-4ea2-990b-\ 910f12f39ffb"], Cell[TextData[{ "The powerful function ", Cell[BoxData[ ButtonBox["InteractiveTradingChart", BaseStyle->"Link", ButtonData->"paclet:ref/InteractiveTradingChart"]],ExpressionUUID-> "6e12dd48-04a6-41d1-8c41-c92a0d557399"], ", introduced in ", StyleBox["Mathematica", FontSlant->"Italic"], " 8, includes practically all the functionality that a chartist may require. \ In this example, we display GE\[CloseCurlyQuote]s share price history for a \ given period. Notice that in the upper area of the graph, we can see a \ trimester at a time and using the bottom part we can move through the entire \ period. We can also choose the time interval (days, weeks or months) and even \ what chart type and indicators to show." }], "Item1", CellChangeTimes->{{3.512792395565881*^9, 3.512792438084313*^9}, { 3.5127924874841385`*^9, 3.5127925578211613`*^9}, {3.5149965179824505`*^9, 3.51499652316166*^9}, {3.5162568930433693`*^9, 3.5162568941784344`*^9}, { 3.5165546299262724`*^9, 3.516554631439475*^9}, {3.5286974909605637`*^9, 3.528697526008112*^9}, {3.528724394364876*^9, 3.52872439701688*^9}, { 3.5291243294419527`*^9, 3.5291245015358524`*^9}, {3.52912478513515*^9, 3.5291248887193317`*^9}, {3.5291251579850025`*^9, 3.5291252423187504`*^9}, {3.5291253100540695`*^9, 3.529125553428096*^9}, { 3.5291255863661532`*^9, 3.5291255871149545`*^9}, {3.5291256774435067`*^9, 3.529125679908311*^9}, {3.632077038275524*^9, 3.6320770692896504`*^9}, { 3.65328367223104*^9, 3.653283824746943*^9}, {3.653283868369834*^9, 3.653283965125226*^9}, {3.6532840694094152`*^9, 3.6532841059874983`*^9}, { 3.653284150148926*^9, 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As a matter of fact, all the efforts that have \ been made trying to predict financial markets have produced unsatisfactory \ results. 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When an organization needs capital, instead of borrowing from banks, they \ can issue bonds. Bonds can be considered a type of loan in which the lenders \ are the ones purchasing them. Those lenders can usually be anyone. There are \ different types of bonds. Normally they pay a fixed amount of interest at \ predetermined time intervals: annually, half-annually, quarterly or even \ monthly. 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\t\[OpenCurlyDoubleQuote]RedemptionValue\[CloseCurlyDoubleQuote]\t\ redemption value \t\[OpenCurlyDoubleQuote]InterestRate\[CloseCurlyDoubleQuote]\t\tyield \ to maturity or yield rate \t\[OpenCurlyDoubleQuote]Settlement\[CloseCurlyDoubleQuote]\t\t\ settlement date \t\[OpenCurlyDoubleQuote]DayCountBasis\[CloseCurlyDoubleQuote]\tday \ count convention\ \>", "Item1Paragraph", CellChangeTimes->{{3.528612000350604*^9, 3.528612007152216*^9}, { 3.5286120568738995`*^9, 3.528612070346322*^9}, {3.529126530596442*^9, 3.5291266724006915`*^9}, {3.529126725772259*^9, 3.5291267550223107`*^9}, { 3.5291268217871075`*^9, 3.529126830133122*^9}, {3.5291268821677437`*^9, 3.5291268895621567`*^9}, {3.5291269702698617`*^9, 3.5291269869930906`*^9}, { 3.6533501075497723`*^9, 3.653350166035597*^9}},ExpressionUUID->"7df7149e-6e2a-4077-8691-\ 28a4b79ec69d"], Cell["Let\[CloseCurlyQuote]s see some examples.", "Texto AM", CellChangeTimes->{{3.653352034996916*^9, 3.653352038053343*^9}},ExpressionUUID->"e7e37766-b92b-47df-b2e5-\ c0ad42740291"], Cell["\<\ The yield to maturity of a \[Euro]1,000 30-year bond maturing on February 28, \ 2019, with a coupon of 6% paid quarterly that was purchased on January 6, \ 2013 for \[Euro]900 would be:\ \>", "Item1", CellChangeTimes->{ 3.52861169805009*^9, {3.528611742468567*^9, 3.528611746805374*^9}, { 3.5286120401118703`*^9, 3.5286120493826857`*^9}, {3.528612172542595*^9, 3.528612174149398*^9}, {3.6533520582967987`*^9, 3.653352118307444*^9}, { 3.6533521586256027`*^9, 3.6533522317619267`*^9}, {3.6533522789056063`*^9, 3.653352345214473*^9}, {3.65335259941726*^9, 3.6533526022318068`*^9}, { 3.653352736096972*^9, 3.653352816148901*^9}, {3.653363488249234*^9, 3.6533634982167997`*^9}, {3.762577942537393*^9, 3.762577948505725*^9}, { 3.762577988656766*^9, 3.76257801565588*^9}}, CellID->757559835,ExpressionUUID->"a886a89d-a0ef-41bb-adb8-9fad33742f5e"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FindRoot", "[", 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3.68856793866887*^9},ExpressionUUID->"a3eca15f-6e00-412c-9a80-\ e9832f42be36"], Cell[TextData[{ "In this example we first compute the price of a derivative using ", StyleBox["Mathematica", FontSlant->"Italic"], "\[CloseCurlyQuote]s existing function and then compare it with the result \ obtained by solving the Black\[Dash]Scholes equation directly" }], "Texto AM", CellChangeTimes->{{3.681514364010161*^9, 3.681514437569271*^9}, { 3.681514574285718*^9, 3.6815146032903967`*^9}, {3.6815376694783688`*^9, 3.681537670870082*^9}, {3.6899127412483196`*^9, 3.6899127549546275`*^9}, { 3.689935264266753*^9, 3.689935275211379*^9}},ExpressionUUID->"621eb742-57da-4d56-8c1d-\ 8703b59aa13c"], Cell[TextData[{ "(", ButtonBox["http://www.wolfram.com/language/11/partial-differential-equations/\ find-the-value-of-a-european-call-option.html", BaseStyle->"Hyperlink", ButtonData->{ URL["http://www.wolfram.com/language/11/partial-differential-equations/\ find-the-value-of-a-european-call-option.html"], None}, ButtonNote-> "http://www.wolfram.com/language/11/partial-differential-equations/find-\ the-value-of-a-european-call-option.html"], "). " }], "Texto AM", CellChangeTimes->{{3.681368251574501*^9, 3.681368253017598*^9}, { 3.681368303874117*^9, 3.681368319918507*^9}, {3.6813689356202126`*^9, 3.681368936626375*^9}, {3.681445056167742*^9, 3.6814450604388094`*^9}, { 3.681445280356923*^9, 3.6814453110822754`*^9}, {3.681511545449955*^9, 3.6815115776982517`*^9}, {3.681513342733316*^9, 3.6815133437519903`*^9}, { 3.6815134415637693`*^9, 3.681513499689301*^9}, {3.681513541869508*^9, 3.6815137097777023`*^9}, {3.681513789672303*^9, 3.681513819567973*^9}, { 3.6815138537193947`*^9, 3.6815139121166058`*^9}, {3.681513971117299*^9, 3.6815140639560843`*^9}, {3.681514098818026*^9, 3.681514274794608*^9}, { 3.6815314450798235`*^9, 3.6815315166360435`*^9}, {3.68991281015613*^9, 3.689912846715125*^9}, {3.689935242483507*^9, 3.6899352452676663`*^9}},ExpressionUUID->"f00dce35-f9e2-41ca-8ac0-\ 76a6b6ab57d0"], Cell[TextData[{ "Let\[CloseCurlyQuote]s start by using ", ButtonBox["FinancialDerivative", BaseStyle->"Link", ButtonData->"paclet:ref/FinancialDerivative"], " to compute the price of a European vanilla call option with the data from \ the previous section: " }], "Item1", CellChangeTimes->{{3.681368251574501*^9, 3.681368253017598*^9}, { 3.681368303874117*^9, 3.681368430928663*^9}, {3.68144462605293*^9, 3.6814448500148935`*^9}, {3.6814449222453737`*^9, 3.681444939422976*^9}, { 3.681511828594331*^9, 3.6815118880834723`*^9}, {3.681511932104941*^9, 3.681511950021364*^9}, {3.6815120267384644`*^9, 3.681512027384344*^9}, { 3.68151261698494*^9, 3.681512653487174*^9}, 3.6815127232047863`*^9, { 3.681512785358479*^9, 3.681512791499173*^9}, {3.681513678747038*^9, 3.6815136885701027`*^9}, {3.681537681461995*^9, 3.681537691773036*^9}},ExpressionUUID->"5197d3cb-a9ed-48c1-98d9-\ 6229531cc33a"], Cell[BoxData[ RowBox[{ RowBox[{"spotPrice", " ", "=", "9.87"}], ";", RowBox[{"euribor12m", "=", "0.00058"}], ";", RowBox[{"vol", "=", "0.528374"}], ";"}]], "Input", CellChangeTimes->{{3.5287837116739607`*^9, 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CellLabel->"Out[9]=",ExpressionUUID->"9647d3a9-d5b9-4b63-9448-d110978b04f6"] }, Open ]], Cell[TextData[{ "Now, let\[CloseCurlyQuote]s do the same computation using the \ Black\[Dash]Scholes equation (To create more visually appealing documents you \ can convert the input cell to the traditional format: ", Cell[BoxData[ FormBox[ RowBox[{ StyleBox["Cell", FontWeight->"Bold"], StyleBox[" ", FontWeight->"Bold"], "\[FilledRightTriangle]", " ", StyleBox["Convert", FontWeight->"Bold"], StyleBox[" ", FontWeight->"Bold"], StyleBox["to", FontWeight->"Bold"], " ", "\[FilledRightTriangle]", " ", StyleBox["TraditionalForm", FontWeight->"Bold"]}], TraditionalForm]],ExpressionUUID-> "4228c2dc-a42b-4ad7-ae06-d12220744749"], "):" }], "Item1", CellChangeTimes->{{3.6814451091288786`*^9, 3.68144511585104*^9}, { 3.6814451532408113`*^9, 3.6814451740752196`*^9}, {3.681511667775701*^9, 3.681511697729526*^9}, {3.681514233347875*^9, 3.681514234243528*^9}, { 3.681514466003708*^9, 3.681514466569558*^9}, 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With the \ exception of ", Cell[BoxData[ ButtonBox[Cell[ "LinearProgramming",ExpressionUUID->"b723d3e6-5b2e-4fda-931f-8f927056128e"], BaseStyle->Dynamic[ If[ CurrentValue["MouseOver"], { "Link", FontColor -> RGBColor[0.854902, 0.396078, 0.145098]}, {"Link"}]], ButtonData->"paclet:ref/LinearProgramming"]],ExpressionUUID-> "4378a095-8fe3-4245-9ab4-755fae439ecf"], ", the syntax for the rest of the functions is very similar: ", StyleBox["f", "Input"], "[{objective function", StyleBox[", constraints", FontSlant->"Italic"], "}, {", StyleBox["variables", FontSlant->"Italic"], "}]." }], "Texto AM", CellChangeTimes->{{3.528528158651555*^9, 3.528528193120967*^9}, { 3.5285282812476587`*^9, 3.5285284117501645`*^9}, {3.5285285546279078`*^9, 3.528528559643629*^9}, 3.5285288344926558`*^9, {3.528716196715414*^9, 3.5287161976982155`*^9}, {3.528716232657877*^9, 3.5287162751991515`*^9}, { 3.528716307148008*^9, 3.5287163251816397`*^9}, {3.655163337068082*^9, 3.655163392300763*^9}, {3.655163433826057*^9, 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the previously mentioned commands:\ \>", "Item1", CellChangeTimes->{{3.4650406051066093`*^9, 3.4650406490674095`*^9}, { 3.465041100562609*^9, 3.465041141247409*^9}, {3.465041294720209*^9, 3.465041315452609*^9}, {3.465041411720209*^9, 3.465041415854209*^9}, 3.525255006606313*^9, {3.5287164248034143`*^9, 3.5287164345690317`*^9}, { 3.528716651504013*^9, 3.5287166846072707`*^9}, {3.6551635945521173`*^9, 3.655163606567254*^9}, {3.664165995537632*^9, 3.664165997206456*^9}}, CellTags->{ "S3.9.9", "9.5"},ExpressionUUID->"d7460c1a-521d-45f9-b56e-695674821590"], Cell[CellGroupData[{ Cell["\<\ {NMaximize[{ob,c1,c2}, var], Maximize[{ob,c1,c2}, var], FindMaximum[{ob,c1,c2}, var]}\ \>", "Input", CellChangeTimes->{{3.4649740667060003`*^9, 3.4649740923992*^9}, { 3.465041155318609*^9, 3.4650412265170093`*^9}, {3.465042037810609*^9, 3.465042055859809*^9}, {3.4938789977498646`*^9, 3.4938790009166703`*^9}, { 3.5285286487234645`*^9, 3.528528699208809*^9}, {3.5287163700473185`*^9, 3.5287163860841465`*^9}, 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Cell[CellGroupData[{ Cell[" Minimize[{ob,c1,c2}, var]", "Input", CellChangeTimes->{{3.4649740667060003`*^9, 3.4649740923992*^9}, { 3.465041155318609*^9, 3.4650412265170093`*^9}, {3.465042037810609*^9, 3.465042079603009*^9}, 3.4938789122151103`*^9, {3.5287168711435986`*^9, 3.528716892110036*^9}, {3.664173073637932*^9, 3.664173078237804*^9}, { 3.664236791082615*^9, 3.664236791579248*^9}}, CellTags->"S3.9.9",ExpressionUUID->"86a701af-18a4-4ae6-a3ad-08371ea8248a"], Cell[BoxData[ RowBox[{"{", RowBox[{"0", ",", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "0"}], ",", RowBox[{"y", "\[Rule]", "0"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.5287168933112373`*^9, 3.6321441274619417`*^9, 3.6627369761120157`*^9, 3.675009607885695*^9, 3.675707923228414*^9, 3.678234148234337*^9, 3.6802819499623504`*^9}, CellTags->"S3.9.9",ExpressionUUID->"8ac7fddf-834e-4cfd-bc3b-1066094125a8"] }, Open ]], Cell[TextData[{ "We can interpret the problem graphically by drawing the plane", Cell[BoxData[ FormBox[ 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Use the mouse to move the graph around to see it from different \ perspectives. \ \>", "Item1Paragraph", CellChangeTimes->{{3.5252551260861473`*^9, 3.525255158255987*^9}, { 3.5285290502311735`*^9, 3.5285290502311735`*^9}, 3.5287170827673707`*^9, { 3.5877076378386836`*^9, 3.5877076431512856`*^9}, {3.587802416039564*^9, 3.587802416070815*^9}, {3.655164628611258*^9, 3.655164687950027*^9}, { 3.655164719149481*^9, 3.655164742610962*^9}},ExpressionUUID->"fe2632b5-7ea7-474d-b293-\ 26aa6ed0ef84"], Cell[TextData[{ "In certain situations we\[CloseCurlyQuote]d like the variables to take only \ integer values. 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As a matter of fact, this command is the most appropriate one for linear \ problems, especially if the number of variables is large. The syntax is: ", Cell[BoxData[ StyleBox[ ButtonBox["LinearProgramming", BaseStyle->"Link", ButtonData->"paclet:ref/LinearProgramming"], FontFamily->"Courier"]],ExpressionUUID-> "c6f62ab1-a8fe-4600-bc56-90132842028c"], "[", StyleBox["c", FontSlant->"Italic"], ", ", StyleBox["m", FontSlant->"Italic"], ", ", StyleBox["b", FontSlant->"Italic"], "] . This function finds the vector ", StyleBox["x", FontWeight->"Bold"], " that minimizes the quantity ", StyleBox["c.x", FontWeight->"Bold"], " subject to the constraints ", StyleBox["m.x", FontWeight->"Bold"], " \[GreaterEqual] ", StyleBox["b", FontWeight->"Bold"], " and ", StyleBox["x ", FontWeight->"Bold"], "\[GreaterEqual] 0. We can limit the values that the variables (some or all \ of them) can take to just integers with ", Cell[BoxData[ StyleBox[ ButtonBox["LinearProgramming", BaseStyle->"Link", ButtonData->"paclet:ref/LinearProgramming"], FontFamily->"Courier"]],ExpressionUUID-> "4d55875a-777d-4303-af91-488bc658a199"], "[..., Integers]." }], "Texto AM", CellChangeTimes->{{3.5254568475204754`*^9, 3.525456875319724*^9}, 3.5285293215645075`*^9, {3.528623880886846*^9, 3.5286239181844373`*^9}, { 3.528718149503353*^9, 3.528718213557065*^9}, {3.65516511342422*^9, 3.6551652794741173`*^9}, {3.655255624977072*^9, 3.6552556823741765`*^9}, { 3.664166285315711*^9, 3.664166286307241*^9}, {3.689220265059286*^9, 3.6892203395975494`*^9}, {3.689220408595496*^9, 3.6892204512269344`*^9}, 3.689577111407222*^9, {3.6899133800970697`*^9, 3.6899134328896036`*^9}, { 3.689935332307645*^9, 3.6899353365558877`*^9}, {3.689991524304401*^9, 3.68999152592517*^9}},ExpressionUUID->"4a049bb8-38a7-486e-8d0a-\ 8ba9b2bb6251"], Cell[CellGroupData[{ Cell[TextData[{ "For comparison purposes, let\[CloseCurlyQuote]s solve the same problem \ using ", Cell[BoxData[ StyleBox[ ButtonBox["LinearProgramming", BaseStyle->"Link", ButtonData->"paclet:ref/LinearProgramming"], FontFamily->"Courier"]],ExpressionUUID-> "f9de4859-6a37-43a3-aea5-f5ed560d2686"], ":" }], "Item1", CellChangeTimes->{{3.525255274599642*^9, 3.5252552792049055`*^9}, { 3.5252553308038564`*^9, 3.525255373191281*^9}, {3.525258081793746*^9, 3.525258086739029*^9}, {3.525456932681025*^9, 3.525456951369858*^9}, { 3.528624052062008*^9, 3.528624052062008*^9}, {3.5287182251478853`*^9, 3.5287182251478853`*^9}, {3.528724726442659*^9, 3.5287248180148196`*^9}, 3.587707680244958*^9, {3.655165335428082*^9, 3.655165359129034*^9}, { 3.664168059505319*^9, 3.664168112725594*^9}, 3.689913446512562*^9},ExpressionUUID->"dc7c0fa4-d228-4c4a-9f73-\ a702f34f38ed"], Cell[TextData[{ "\t", Cell[BoxData[ FormBox[ RowBox[{"x", " ", "+", " ", RowBox[{"2", " ", "y", "\t"}]}], TraditionalForm]],ExpressionUUID-> "d2c4196e-eb3c-45f8-af39-b85ddb067cf6"], "\t\t\[Rule] \t", Cell[BoxData[ FormBox[ RowBox[{"c", ":", " ", RowBox[{"{", RowBox[{"1", ",", " ", "2"}], "}"}]}], TraditionalForm]],ExpressionUUID-> "c32a36ea-8421-4941-b9c2-fe9e0975cebe"], "\n\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "5"}], " ", "x"}], " ", "+", " ", "y"}], " ", "\[Equal]", " ", "7", " "}], TraditionalForm]],ExpressionUUID-> "fee91687-2af9-4356-aaaa-72ea2ab65946"], " \t\[Rule]\t", Cell[BoxData[ FormBox[ RowBox[{"m1", ":", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "5"}], ",", " ", "1"}], "}"}], " \t", RowBox[{"b1", ":", " ", RowBox[{"{", RowBox[{"7", ",", " ", "0"}], "}"}]}]}]}], TraditionalForm]], ExpressionUUID->"b9287ea1-6753-4e26-b18d-7835f0fd8460"], "\n\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"x", " ", "+", " ", "y"}], " ", "\[GreaterEqual]", " ", "26"}], TraditionalForm]],ExpressionUUID->"40ec9d70-9a46-4d30-ac08-edbac7dba662"], " \t\t\[Rule]\t", Cell[BoxData[ FormBox[ RowBox[{"m2", ":", " ", RowBox[{ RowBox[{"{", RowBox[{"1", ",", " ", "1"}], "}"}], "\t ", "b2"}], ":", " ", RowBox[{"{", RowBox[{"26", ",", " ", "1"}], "}"}]}], TraditionalForm]],ExpressionUUID-> "2f238092-aac7-40bb-8315-79914a40cd05"] }], "Example", CellChangeTimes->{{3.4952781865961876`*^9, 3.495278351441677*^9}, { 3.4952783882421417`*^9, 3.4952785738356676`*^9}, {3.5252581063131485`*^9, 3.5252581122574883`*^9}, 3.525456960963875*^9, {3.5286239682635236`*^9, 3.528624038983631*^9}, 3.52871786790315*^9, 3.66416637519774*^9, { 3.664166414957151*^9, 3.66416643377386*^9}, {3.664168570229887*^9, 3.664168598518258*^9}},ExpressionUUID->"f99f8c12-50cb-4b1b-a1a3-\ 5eb17856eeb2"], Cell[TextData[{ "Notice that the syntax to indicate the type of constraint is as follows: {", Cell[BoxData[ FormBox[ SubscriptBox["b", "i"], TraditionalForm]],ExpressionUUID-> "389be074-d2f4-45ca-8026-ba3c6843b5df"], ", 0} if ", Cell[BoxData[ RowBox[{ RowBox[{ SubscriptBox[ StyleBox["m", "TI"], StyleBox["i", "TI"]], ".", StyleBox["x", "TI"]}], "==", SubscriptBox[ StyleBox["b", "TI"], StyleBox["i", "TI"]]}]], "InlineFormula",ExpressionUUID-> "12b466a1-2ec5-4d59-a785-9aa7e964dcb6"], "; {", Cell[BoxData[ FormBox[ SubscriptBox["b", "i"], TraditionalForm]],ExpressionUUID-> "22107e3c-d58f-44d9-ba5d-9e2f97585802"], ", 1} if ", Cell[BoxData[ RowBox[{ RowBox[{ SubscriptBox[ StyleBox["m", "TI"], StyleBox["i", "TI"]], ".", StyleBox["x", "TI"]}], "\[GreaterEqual]", SubscriptBox[ StyleBox["b", "TI"], StyleBox["i", "TI"]]}]], "InlineFormula",ExpressionUUID-> "e5efe12b-cdf0-4232-8658-4c17ee9661ce"], " and {", Cell[BoxData[ FormBox[ SubscriptBox["b", "i"], TraditionalForm]],ExpressionUUID-> "8d57b8eb-91a0-473f-af22-e5ab5e85569c"], ", ", Cell[BoxData[ FormBox[ RowBox[{"-", "1"}], TraditionalForm]],ExpressionUUID-> "6ccbd2a1-1777-4aa1-9d18-a6cf7e8dcb02"], "} if ", Cell[BoxData[ RowBox[{ RowBox[{ SubscriptBox[ StyleBox["m", "TI"], StyleBox["i", "TI"]], ".", StyleBox["x", "TI"]}], "\[LessEqual]", SubscriptBox[ StyleBox["b", "TI"], StyleBox["i", "TI"]]}]], "InlineFormula",ExpressionUUID-> "e04b6755-4220-4c41-8641-e779144addaa"], "." }], "Item1Paragraph", CellChangeTimes->{{3.6642530147777996`*^9, 3.664253018697091*^9}, { 3.664253065151531*^9, 3.6642530710313616`*^9}, {3.664253103662318*^9, 3.6642532069366603`*^9}, {3.6642532434643545`*^9, 3.664253272385768*^9}, { 3.6642533232637367`*^9, 3.6642535700688515`*^9}, {3.66425361163491*^9, 3.664253788970435*^9}, {3.6642538340364733`*^9, 3.6642539297611084`*^9}, { 3.6642539603056555`*^9, 3.6642540971502676`*^9}, {3.664491879663018*^9, 3.664491885115497*^9}, {3.664491930290372*^9, 3.664491979629559*^9}, { 3.664492030616745*^9, 3.664492056021702*^9}, {3.664492092637241*^9, 3.664492094948207*^9}, {3.6895771984141984`*^9, 3.6895772094458294`*^9}, { 3.690192139193661*^9, 3.690192173769639*^9}},ExpressionUUID->"68123774-3cae-4ca4-8095-\ 4cabd5693a8d"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"LinearProgramming", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "5"}], ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"7", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"26", ",", "1"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"3", ",", "Infinity"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "Infinity"}], "}"}]}], "}"}], ",", "Integers"}], "]"}], "//", "Quiet"}]], "Input", CellChangeTimes->{{3.6641681629308443`*^9, 3.664168210337381*^9}}, CellID->14420703,ExpressionUUID->"fda3fc5d-b719-4550-a9b9-3d456064bf07"], Cell[BoxData[ RowBox[{"{", RowBox[{"4", ",", "27"}], "}"}]], "Output", CellChangeTimes->{ 3.632144127649435*^9, 3.6551656207751093`*^9, 3.6627369762280984`*^9, { 3.664168167084408*^9, 3.664168210895747*^9}, 3.664168274115459*^9, 3.6750096080084705`*^9, 3.6757079233652954`*^9, 3.6782341483658752`*^9, 3.68028195017831*^9}, ImageSize->{73, 32}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}},ExpressionUUID->"423e654f-cc28-48e8-aa41-35ecac6125b2"] }, Open ]], Cell["Next we\[CloseCurlyQuote]ll show some examples for nonlinear \ optimization. ", "Texto AM", CellChangeTimes->{{3.5252585411140175`*^9, 3.52525858609059*^9}, { 3.5285294399574056`*^9, 3.528529530162263*^9}, {3.5287245053434706`*^9, 3.52872461913007*^9}, {3.6281774049452963`*^9, 3.6281774506995816`*^9}, { 3.655165455654097*^9, 3.655165467606546*^9}, 3.664166842622801*^9},ExpressionUUID->"7ed17e44-dac6-4601-8109-\ 68d36c781d55"], Cell[BoxData[ RowBox[{"Clear", "[", "\"\<`Global`*\>\"", "]"}]], "Input", CellChangeTimes->{{3.5287164816967144`*^9, 3.5287165096061635`*^9}, { 3.528716543380223*^9, 3.5287165469838295`*^9}},ExpressionUUID->"0dcb76f0-30d2-4e0e-9e92-\ d8e83aba983f"], Cell[TextData[{ "Here is another example of nonlinear optimization, in this case for finding \ the global minimum (", Cell[BoxData[ ButtonBox[Cell[ "Minimize",ExpressionUUID->"74cef59e-bb84-4582-ada7-3a25919be950"], BaseStyle->Dynamic[ If[ CurrentValue["MouseOver"], { "Link", FontColor -> RGBColor[0.854902, 0.396078, 0.145098]}, {"Link"}]], ButtonData->"paclet:ref/Minimize"]],ExpressionUUID-> "b41590eb-b137-4f94-ae4a-5b70d1e1717e"], "). The objective function is ", Cell[BoxData[ FormBox[ RowBox[{"Exp", "(", RowBox[{ RowBox[{"-", "x"}], " ", "y"}], ")"}], TraditionalForm]],ExpressionUUID-> "cb17f899-e411-4388-a882-80eb3025e796"], " with the constraint that ", Cell[BoxData[ FormBox[ RowBox[{"x", ",", " ", "y"}], TraditionalForm]],ExpressionUUID-> "8e4ba1fe-48b6-4baf-8fe4-cca7c23a0b16"], " \[Element] a Circle centered in {0, 0} and with a radius ", Cell[BoxData[ FormBox[ RowBox[{"r", "=", "1"}], TraditionalForm]],ExpressionUUID-> "12ce8f3b-93bf-473e-8de9-a05aea252b82"], ". We show the result, both numerically and graphically. 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One of the most \ famous examples is the ", StyleBox["Traveling Salesman Problem", FontSlant->"Italic"], " (TSP). This problem can be defined as follows: A traveler would like to \ visit ", StyleBox["N", FontSlant->"Italic"], " cities starting and finishing in the same arbitrarily chosen one, \ minimizing the total distance traveled and passing through each city only \ once. If you think about it, there are many real-world problems that are \ actually equivalent to the TSP: route optimization (transportation, \ logistics), optimum network layout (trains, roads, electricity), even the \ connections inside microprocessors to minimize calculation time. " }], "Texto AM", CellChangeTimes->{{3.5286041226156006`*^9, 3.5286043712332373`*^9}, { 3.528604405256897*^9, 3.5286045366091275`*^9}, {3.5286048040384016`*^9, 3.5286051229653616`*^9}, {3.52860521868713*^9, 3.5286052437095737`*^9}, { 3.528864610264906*^9, 3.52886461252691*^9}, {3.5288646625715156`*^9, 3.5288647910699415`*^9}, {3.528864853329651*^9, 3.5288648586034603`*^9}, { 3.6551043417342196`*^9, 3.655104342535265*^9}, {3.6551043912640524`*^9, 3.655104414247367*^9}, {3.65510449408992*^9, 3.6551045234963727`*^9}, { 3.655104555915631*^9, 3.6551046713780375`*^9}, {3.655104783349449*^9, 3.6551049366105285`*^9}, {3.655105035595134*^9, 3.655105106937668*^9}, { 3.6551051403175936`*^9, 3.6551051444380007`*^9}, {3.655105220567979*^9, 3.655105338254594*^9}, {3.6551054176569357`*^9, 3.655105418405737*^9}, { 3.6551054525775995`*^9, 3.6551054722936373`*^9}, {3.6551055025428963`*^9, 3.6551055189807262`*^9}, {3.6551058486303453`*^9, 3.655105892933427*^9}, 3.6551066747112417`*^9, {3.6552559126534443`*^9, 3.655255918113454*^9}, { 3.664233355572418*^9, 3.664233366739937*^9}, {3.6642334254516373`*^9, 3.664233497383479*^9}, {3.690192979033697*^9, 3.6901929797947407`*^9}},ExpressionUUID->"a43aaf5e-4572-41a5-ab0e-\ 5fdca376f146"], Cell[TextData[{ "Mathematically, the problem consists of finding a permutation P = {", Cell[BoxData[ FormBox[ SubscriptBox["c", "0"], TraditionalForm]],ExpressionUUID-> "fc46a0dc-1bd4-40f1-84a7-da6225fece41"], ", ", Cell[BoxData[ FormBox[ SubscriptBox["c", RowBox[{"1", " "}]], TraditionalForm]],ExpressionUUID-> "22144a0c-92b4-4736-ad7f-5bbc910c591e"], ",...,", Cell[BoxData[ FormBox[ RowBox[{" ", SubscriptBox["c", RowBox[{"n", "-", "1"}]]}], TraditionalForm]],ExpressionUUID-> "7fdea335-ac50-4323-ad1a-843d33cd66b4"], "} such that ", Cell[BoxData[ FormBox[ SubscriptBox["d", "P"], TraditionalForm]],ExpressionUUID-> "ba798da6-daee-47ea-b052-9cedde673fc5"], " = ", Cell[BoxData[ FormBox[ RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], RowBox[{"n", "-", "1"}]], RowBox[{"d", "[", RowBox[{ SubscriptBox["c", "i"], ",", SubscriptBox["c", RowBox[{"i", "+", "1"}]]}], "]"}]}], TraditionalForm]],ExpressionUUID-> "ab428ba4-dec2-4c35-90a6-36441ee0aede"], " would be a minimum, with ", Cell[BoxData[ FormBox[ SubscriptBox["d", "ij"], TraditionalForm]],ExpressionUUID-> "cd678e5f-324b-4368-9b36-f455c2b07d27"], " representing the distance from city ", StyleBox["i", FontSlant->"Italic"], " to city ", StyleBox["j", FontSlant->"Italic"], "." }], "Texto AM", CellChangeTimes->{{3.5286041226156006`*^9, 3.5286041450172396`*^9}, 3.528604811323614*^9, {3.528605342973548*^9, 3.528605408930464*^9}, { 3.5286054530857415`*^9, 3.5286055371698895`*^9}, {3.52860559439079*^9, 3.52860563442046*^9}, {3.528605728067425*^9, 3.5286057456018553`*^9}, { 3.528864867058675*^9, 3.528864867776276*^9}, {3.655105990614951*^9, 3.655106056584792*^9}, {3.655106111865013*^9, 3.6551061122942142`*^9}, { 3.689578580670259*^9, 3.689578595614114*^9}, {3.6895787984777164`*^9, 3.6895787994697733`*^9}, {3.689991902194172*^9, 3.6899919169371367`*^9}, { 3.6934892403342495`*^9, 3.693489241360454*^9}},ExpressionUUID->"ca35bcef-f67a-4f18-bbea-\ c70a1c60afa3"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ CounterBox["BookChapterNumber"], ".", CounterBox["Section"], ".", CounterBox["Subsection"], " A Tour Around South American Cities" }], "Subsection", CellChangeTimes->{ 3.525255611161892*^9, {3.528529959514256*^9, 3.5285300130777845`*^9}, { 3.528544713589114*^9, 3.528544718471923*^9}, {3.6541325318809204`*^9, 3.6541325374345303`*^9}, {3.654646140287301*^9, 3.6546461414973702`*^9}, { 3.6812872127086687`*^9, 3.68128722830469*^9}, {3.6813695048007565`*^9, 3.6813695348629775`*^9}, {3.68142163037784*^9, 3.6814216365854387`*^9}, { 3.688567999315529*^9, 3.6885679997309523`*^9}},ExpressionUUID->"b389985c-b8c4-4125-821e-\ 9f4254b1bcac"], Cell["\<\ The next example is about organizing a trip to several cities in South \ America. In what order should we visit them to minimize the total distance \ traveled?\ \>", "Texto AM", CellChangeTimes->{{3.525259560233308*^9, 3.52525961569848*^9}, { 3.5286016645559273`*^9, 3.5286016650599566`*^9}, {3.528601910609001*^9, 3.5286019365664854`*^9}, {3.5286027929414673`*^9, 3.528602793300488*^9}, { 3.5288654849203606`*^9, 3.528865486261963*^9}, {3.655156881486291*^9, 3.655156987004084*^9}, 3.689220977138015*^9},ExpressionUUID->"4467813c-7096-4a52-a150-\ cd9ca9381e4f"], Cell["\<\ The cities we\[CloseCurlyQuote]re visiting are the following (we indicate \ both, the cities and their respective regions and countries to avoid \ ambiguity):\ \>", "Item1", CellChangeTimes->{{3.4950254430723104`*^9, 3.4950255104332285`*^9}, 3.4950819725698996`*^9, {3.4950821065775642`*^9, 3.4950821139689875`*^9}, { 3.5252595487316504`*^9, 3.525259554570984*^9}, {3.525259623195909*^9, 3.5252597245067034`*^9}, {3.528600874616565*^9, 3.5286009063002205`*^9}, { 3.5286015937628784`*^9, 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{\"Quito\", \"Pichincha\", \"Ecuador\"}], Entity[\"City\", {\"Santiago\", \"Metropolitana\", \"Chile\"}]};\ \>", "Input", CellChangeTimes->{{3.6812869499089284`*^9, 3.681286954456707*^9}},ExpressionUUID->"b0c006fb-0fb9-4135-a4fb-\ 4a0a7f0795e5"], Cell["Now we can calculate the best visiting order:", "Item1", CellChangeTimes->{{3.4950806089289036`*^9, 3.495080631120173*^9}, { 3.495080873504037*^9, 3.4950808745680976`*^9}, 3.5286019959138803`*^9, { 3.528602067955001*^9, 3.528602071419199*^9}, {3.528602222274827*^9, 3.5286022749218383`*^9}, {3.5286024310207667`*^9, 3.5286024715720863`*^9}, {3.5288660229879055`*^9, 3.528866037355531*^9}, { 3.528866506589755*^9, 3.5288665531246367`*^9}, {3.655157236328018*^9, 3.6551572527109413`*^9}, {3.664234228758039*^9, 3.6642342298858337`*^9}},ExpressionUUID->"5c79df03-ccdb-4f3b-8ec0-\ c426eff32e20"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"order", "=", RowBox[{"Last", "[", RowBox[{"FindShortestTour", "[", RowBox[{"GeoPosition", "[", "cities", 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